Our definition of content similarity (or content loss) was motivated by the phenomena of pareidolia, which is when humans perceive arrangements of arbitrary shapes and textures to represent a semantic object (for example seeing animals made of clouds, or a face in a car's grille). This phenomena implies that our perception is at least partially based on relative appearance, rather than absolute appearance, which allows us to recognize a shape as representing an object regardless of the texture. Self-similarity [1]} is a formalizes this idea to define a local feature descriptor, where a feature vector at a particular locations
is transformed into a vector of distances from other feature vectors at fixed spatial offsets. In this work we consider self-similarity to be a global phenomena, and a feature vector at a particular locations
is transformed into a vector of distances from all other feature vectors. Content similarity is then the \(L_1\)  distance between two such tensors of global self-similarity features.
Defining content similarity in this way helped disconnect it from
pixels' precise values. Concretely it makes the distance between two content representations invariant to translations and orthonormal affine transformations in feature space (when applied across all spatial positions). This additional invariance makes it easier to satisfy than definition of content similarity used in prior work, distance between raw features, and results in outputs which maintain the perceived semantics and spatial layout of the content image despite being highly stylized.
